`SpatialLedger`

definition

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module: IndisputableMonolith.RRF.Foundation.Gravity
domain: RRF
line: 26 · github
papers citing: none yet

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IndisputableMonolith.RRF.Foundation.Gravity on GitHub at line 26.

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formal source

  23/-! ## Local Ledger (specific to gravity context) -/
  24
  25/-- A local ledger: ledger density at a spatial point. -/
  26structure SpatialLedger where
  27  /-- Transaction density (transactions per unit volume). -/
  28  density : ℝ
  29  /-- Density is non-negative. -/
  30  density_nonneg : 0 ≤ density
  31  /-- Total charge at this point. -/
  32  charge : ℤ
  33  /-- Local balance constraint. -/
  34  balanced : charge = 0
  35
  36/-- The empty (vacuum) ledger. -/
  37def vacuumLedger : SpatialLedger := {
  38  density := 0,
  39  density_nonneg := le_refl 0,
  40  charge := 0,
  41  balanced := rfl
  42}
  43
  44/-- A non-vacuum ledger with mass. -/
  45def massiveLedger (d : ℝ) (hd : 0 < d) : SpatialLedger := {
  46  density := d,
  47  density_nonneg := le_of_lt hd,
  48  charge := 0,
  49  balanced := rfl
  50}
  51
  52/-! ## Mass from Ledger -/
  53
  54/-- Mass is ledger density (the key identification). -/
  55def massFromSpatialLedger (L : SpatialLedger) : ℝ := L.density
  56

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